Cumulative Exam Answers

The perimeter of triangle ABC is 82 inches. The triangle is rotated about a line that passes through points B and D.

Line EF is tangent to circle G at point A.

Triangle J K L is shown. Angle K L J is a right angle. The length of hypotenuse K J is 10.9 centimeters and the length of L J is 8.9 centimeters. Angle L K J is x.

Two similar cylinders have surface areas of 24 cm2 and 54 cm2. The volume of the smaller cylinder is 16 cm3.What is the volume of the larger cylinder?

Quadrilateral ABCD is shown on the grid.

Cheng likes a modern lawn sculpture made of four identical solid right pyramids with square bases. He decides to create an exact copy of the sculpture, so he needs to know what volume of sculpting material to purchase.He measures each edge of each base to be 2 feet. The height of the whole sculpture is 6 feet.

The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2.What is the lateral area of the smaller cylinder?

Jerome found the lengths of each side of triangle QRS as shown, but did not simplify his answers. Simplify the lengths of each side to answer the question. Which statement about triangle QRS is true?

Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters.

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.

The spinner is equally likely to land on any of the five sections.

2 circles labeled Set A and Set B overlap. Set A contains 1, set B contains 3, and the overlap of the 2 circles contains 2. The number 4 is outside of the circles.

Ryder shot a model rocket over an area that consists of two grassy areas, shown in green, and an area with no grass, shown in white.

Circle O has a circumference of approximately 28.3 cm.

Two cylinders are similar. The radius of cylinder A is 5.6 inches. The radius of cylinder B is 1.4 inches. If the height of cylinder B is 4 inches, what is the height of cylinder A?

Nico owns 11 instructional piano books. Two are beginner books, six are intermediate books, and three are advanced books.If two books are randomly chosen from the collection, one at a time, and replaced after each pick, what is the probability that he first chooses an advanced book and then chooses a beginner book?

Ariana, Boris, Cecile, and Diego are students in the service club. Three of the four students will be chosen to attend a conference.Which choice represents the sample space, S, for this event?

A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm.

Point A has an x-coordinate of 7 and lies below the x-axis on a circle with a center at (0, 0) and a radius of 8.

Consider the following sets.U = {all triangles}E = {x|x ∈ U and x is equilateral}I = {x|x ∈ U and x is isosceles}S = {x|x ∈ U and x is scalene}A = {x|x ∈ U and x is acute}O = {x|x ∈ U and x is obtuse}R = {x|x ∈ U and x is right}Which is a subset of I?

Which statement describes whether a right triangle can be formed using one side length from each of these squares?

Figure ABCD is a square. Prove BD ≅ AC. Statements Reasons1.ABCD is a square1.given2.∠DAB, ∠ABC, ∠BCD, and ∠CDA are right angles2.definition of a square3.∠DAB ≅ ∠ABC ≅ ∠BCD ≅ ∠CDA3.right angles are congruent4.AB ≅ BC ≅ CD ≅ DA4.?5.△BAD ≅ △ABC5.SAS6.BD ≅ AC6.CPCTCWhat is the missing reason in the proof?

Which statements about the cylinder are true? Select two options.

Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25o angle with the ground and when the string makes a 45o angle with the ground? Round to the nearest tenth.

Which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle?